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Suppose that X has a hypergeometric distribution with N = 2,000, K = 800, and n = 200. Find the probability P(X ≤ 70) based on the corresponding hypergeometric distribution and approximate normal distribution. Is the normal approximation reasonable?

Suppose that X has a hypergeometric distribution with N = 2,000, K = 800, and n = 200. Find the probability P(X ≤ 70) based on the corresponding hypergeometric distribution and approximate normal distribution. Is the normal approximation reasonable?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
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8. Suppose that X has a hypergeometric distribution with N = 2,000, K = 800, and n = 200. Find the probability P(X ≤70) based on the corresponding hypergeometric distribution and approximate normal distribution. Is the normal approximation reasonable?
Transcribed Image Text:8. Suppose that X has a hypergeometric distribution with N = 2,000, K = 800, and n = 200. Find the probability P(X ≤70) based on the corresponding hypergeometric distribution and approximate normal distribution. Is the normal approximation reasonable?
•Types of functions to express probability distribution (a) Probability Mass Function (PMF) f(x) = P(x = x) (b) Cumulative Distribution Functions (CDF) f(x) = P(X ≤ x) Mean M = { xf(x) Variance 0² = [x²f (x) - μ² Standard Deviation. 0x Tot Discrete Uniform Distribution f(x) = //12 M = 0² = b+ a 2 (b-a+1)² 12 •Binomial Distribution (f(x) = (~) p² (1-P)^-x с пр np(1-P) 1• Hypergeometric Distribution (*) (*) (~) f(x) = и = пр 8² = np(1-P/(N=1) where K/N P= ·Poisson Distribution -^+ (^T)* X! f(x) = e M = AT 0² = NT Where N = population size sample size /no. of trials P probability - p = probability of success on a single trial K = no. of successes in the population in the sample of X - no. successes
Transcribed Image Text:•Types of functions to express probability distribution (a) Probability Mass Function (PMF) f(x) = P(x = x) (b) Cumulative Distribution Functions (CDF) f(x) = P(X ≤ x) Mean M = { xf(x) Variance 0² = [x²f (x) - μ² Standard Deviation. 0x Tot Discrete Uniform Distribution f(x) = //12 M = 0² = b+ a 2 (b-a+1)² 12 •Binomial Distribution (f(x) = (~) p² (1-P)^-x с пр np(1-P) 1• Hypergeometric Distribution (*) (*) (~) f(x) = и = пр 8² = np(1-P/(N=1) where K/N P= ·Poisson Distribution -^+ (^T)* X! f(x) = e M = AT 0² = NT Where N = population size sample size /no. of trials P probability - p = probability of success on a single trial K = no. of successes in the population in the sample of X - no. successes
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